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Give an example of a quadratic function that has zeroes at $x=2$ and $x=4$, and that takes the value $6$ when $x=3$. Write your answer in expanded form "ax^2 + bx + c", where a,b,c are replaced by appropriate numbers.

 Mar 29, 2021
 #1
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We  can write

 

y =  a ( x - 2) ( x - 4)       and we  know  that  ( 3, 6)  is on the graph  so

 

6  =  a ( 3 - 2) ( 3 - 4)

 

6  = -1 a

 

a  =  -6

 

So  we  have

 

y  = -6  ( x - 2) ( x - 4)

 

y  =  -6  ( x^2 - 6x  + 8)

 

y =  -6x^2  + 36x  -  48

 

See  the  graph here :   https://www.desmos.com/calculator/puneh6dg7u

 

cool cool cool

 Mar 29, 2021

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